Relativity of Mass According to Newtonian mechanics the mass of a body is unaffected with change in velocity. But space and time change…….. Therefore “mass” of a body is no longer be unaffected

When v is small as compared to c, v2/c2 <<<1 Relativity of Mass When v is small as compared to c, v2/c2 <<<1  m = m0 i.e. at velocities much smaller than c the mass of the moving object is same as the mass at rest. When v is comparable to c, the 1- v2/c2 < 1 , m > m0  mass of the moving object is greater than at rest. When v c, v2/c2 1 , so m =  or imaginary. This is non sense concept.

Relation between Mass and Energy Limiting Case: When v << c Limiting Case: When v  c K.E. tends to infinity.  to accelerate the particle to the speed of light infinite amount of work would be needed to be done .

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Relativity of Mass Mass at rest. Relativistic mass Proof: do it yourself Note: Length contraction, Time Dilation Rest mass is least Numerical: A stationary body explodes in to two fragments each of mass 1 kg that move apart at speeds of 0.6c relative to the original body. Find the mass of the original body. Ans: 2.5 kg

Examples of mass-energy equivalence Pair Production: when a photon of energy equal to or greater than 1.02 MeV passes close to an atomic nucleus, it disappears and a pair of electron and positron is created i.e.  (Gamma Photon) =e- (electron) + e+ (positron) Positron is a particle of same mass as electron but equal and opposite charge. (2) Pair Annihilation: when an electron and positron come close together, they annihilate each other and equal amount of energy is produced in the form of a pair of - ray photons. e- (electron) + e+ (positron) =  + 

Examples of mass-energy equivalence Pair Production: when a photon of energy equal to or greater than 1.02 MeV passes close to an atomic nucleus, it disappears and a pair of electron and positron is created i.e.  (Gamma Photon) =e- (electron) + e+ (positron) Positron is a particle of same mass as electron but equal and opposite charge. (2) Pair Annihilation: when an electron and positron come close together, they annihilate each other and equal amount of energy is produced in the form of a apir of - ray photons. e- (electron) + e+ (positron) =  + 

Relation between Total energy (E) and momentum(p)

Relation between Kinetic energy (K) and momentum (p) If v<<c, that is , p<<moc2 , then Neglecting higher order terms of binomial expansion, we get  Limiting value of Relativistic Kinetic Energy

Limiting value of Relativistic kinetic energy Relativistic kinetic energy is Expanding by Binomial theorem If v<<c i.e. v/c<<1 So This is expression for kinetic energy in non relativistic case.

Mass less Particle? 1) When m0=o and v<c, E=0, p=0 2) When m0=o and v=c, E=0/0, p=0/0 indeterminate form, hence must have E and p.

Answer : is Photon. Mass less Particle? A particle which has zero rest mass

Units of energy, mass and momentum Energy; eV, keV, MeV, GeV Mass; MeV/c2, Momentum: MeV/c Rest mass Energy of Electron: m0c2=0.51MeV Proton: m0c2=938 MeV Neutron: m0c2=931 MeV Photon: m0c2=0 as massless particle

Ex : Find the mass and speed of 2MeV electron. m=3.55  10-30kg v=2.90  108 ms-1 Ex: Calculate the speed of an electron accelerated through a potential difference of 1.53106 volts. Given c=3108 m/sec, mo=9.110-31Kg, and e= 1.610-19 Coulomb v=0.968c Ex: A body whose specific heat is 0.2kcal/kg-oC is heated through 100oC. Find the % increase in its mass. % increase =9.3310-11 %

Summary Special theory of relativity Basic Postulates Galilean transformation equations: v << c Lorentz transformation equations: v ≈ c Length contraction: Time dilation: Addition of velocities Rest mass is least Energy –mass relationship Mass-less particle.

Summary